Cai, Jeng and Jin studied the setting (REF ) in [1]}. They derived the optimal phase transition curve \(\rho (\beta ;\sigma )\)  and showed that it is attained by HC of the P-values (REF ). The case where \(\sigma ^2=1\)  was initially studied in [2]}, [3]}, [4]}; for this case Theorems REF -REF  follows from [4]}.
